At present, the development of generation-after-next Extreme Ultraviolet Lithography (EUVL) is being conducted. As elemental technologies for EUVL systems, the five items of EUV light sources, aspherical optical systems, exposure apparatuses, multilayered photomasks, and photoresist processes can be cited, and the development of those technologies is being conducted in parallel. The most essential and important issue in this development of EUVL systems is to develop ultra-low-expansion glasses as the basic substrate material suitable for optical systems and photomasks. At the same time, measurement and evaluation technologies for accurately ascertaining and analyzing the materials characteristics are vital to the development of those materials.
In EUVL systems, thermal stability in the sub-nanometer range is required for optical lens materials and photomask substrate materials. Specifically, ultra-low-expansion glasses having coefficients of thermal expansion (CTE) not exceeding ±5 ppb/K at the desired temperature (e.g. 22±3° C. in the photomask substrate) become necessary (Non-Patent Reference 1). Here, if the length of a solid at 0° C. is taken to be L0 and the length at a temperature T° C. is taken to be L, the coefficient of thermal expansion is given as (dL/dT)/L0. At present, two types of TiO2—SiO2 glass and Li2O—Al2O3—SiO2 crystallized glass can be cited as commercially available ultra-low-expansion glasses and are used conventionally as materials for lenses for large astronomical telescopes and semiconductor manufacturing apparatuses (steppers). The former glass realizes an ultra-low expansion coefficient by an adjustment of the ratio of SiO2 and TiO2, and the latter glass realizes it by an adjustment of the crystallization process (annealing temperature and time) in addition to that of the chemical composition ratio (Non-Patent Reference 1 and Non-Patent Reference 2). Even with the best grade among these glasses, the specification for the coefficient of thermal expansion stands at ±20 ppb/K (distribution in a glass ingot; ±10 ppb/K), which is insufficient for the specification for ultra-low-expansion glass for EUVL systems of within ±5 ppb/K at the desired temperature. Recently, manufacturing companies in Japan and other countries have started to carry out trial manufacture of EUVL-grade ultra-low-expansion glasses. For the development of those materials, a measurement accuracy of ±0.2 ppb/K (±σ, σ being the standard deviation) or less with respect to the coefficient of thermal expansion is required (Non-Patent Reference 1).
At present, a number of methods are proposed as methods of evaluating coefficients of thermal expansion of substrates for EUVL use. As a method of directly measuring coefficients of thermal expansion, there is the method of using a dilatometer or the like. These days, products using a laser have been developed, but with the best products having an accuracy of ±5 ppb/K, this is insufficient. Currently, development is being conducted with a target of ±1 ppb/K, but an improvement beyond this level cannot be expected. In addition, the fact that this method requires specimens of a special shape (e.g. 100 mm (L)×6 mm φ), and the fact that, for the purpose of the measurements, destruction is entailed and surface distribution measurements with respect to actual specimens are impossible, etc., are problems from the point of view of materials evaluation methods and quality control.
Moreover, there are evaluation methods taking advantage of the fact that there are linear relationships between the coefficient of thermal expansion of an ultra-low-expansion glass and its other physical and chemical properties, ultrasonic velocity (Non-Patent Reference 3), chemical composition ratio and refractive index (Non-Patent Reference 1). For the evaluation of the coefficient of thermal expansion based on longitudinal-wave velocity measurements using the ultrasonic pulse echo method, chemical composition ratio measurements using the X-ray fluorescence method, the electron probe microanalysis method, the radio-frequency inductively-coupled plasma (ICP) emission analysis method or the like, and refractive index measurements etc. using an interferometer, respective accuracies of ±0.4 ppb/K, ±2 ppb/K, and ±0.023 ppb/K are obtained (Non-Patent Reference 1). However, as for the method based on measurements of the longitudinal wave velocity or the refractive index, this accuracy can not be obtained unless big specimens having a thickness of 100 mm are used, and also, only an average value can be obtained in the thickness direction. In this case, for the evaluation of specimens in which there exist periodic striae, which have developed into a problem in TiO2—SiO2 glass, it is impossible to obtain the distribution of thermal expansion coefficients corresponding to the periodicity of the striae. Also, in order to measure longitudinal-wave velocity, a measurement of the thickness of the specimen must also be performed, something which takes an unusual effort. Further, the dimensions of photomask substrates for EUVL use being 152 mm×152 mm×6.35 mmt, a direct application to these dimensions causes the accuracy to decline markedly (approximately 18 times), due to the thickness.
Regarding technologies of evaluation of ultra-low-expansion glasses for EUVL use, it is required that it be possible to nondestructively evaluate a specimen with shapes actually used in EUVL systems and also, since optical systems are of a reflective type, that it be possible to make evaluations in the proximity of the surface of the specimen, and to evaluate the distribution of its characteristics, as well as to mention the requirements of a high measurement accuracy with respect to coefficients of thermal expansion and a high spatial resolution.
As a new technology for analyzing and evaluating substances and materials, an ultrasonic material characterization system was developed (Non-Patent Reference 4), and there is the possibility that this evaluation technology can overcome the aforementioned problems. In particular, a quantitative measurement method (the V(z) curve analysis method) using focused ultrasonic waves is valid. This is a method which performs a materials evaluation by measuring the propagation characteristics (phase velocity VLSAW and propagation attenuation αLSAW) of leaky surface acoustic waves (LSAW) excited on a specimen surface loaded with water, or the propagation characteristics (phase velocity VLSSCW and propagation attenuation αLSSCW) of leaky surface-skimming compressional waves (LSSCW). According to the present technique, a highly accurate measurement of the distribution of the characteristics of the whole glass substrate surface in a non-destructive and contactless manner is possible. For the measurements, an ultrasonic point-focus beam (PFB) and an ultrasonic line-focus beam (LFB) can be used, but here we will proceed with the explanation by considering an LFB ultrasonic material characterization system (refer to Non-Patent Reference 4 and Non-Patent Reference 5).
The LFB ultrasonic material characterization system can obtain the propagation characteristics of leaky acoustic waves propagating on the boundary between the water and the specimen by analyzing the V(z) curve obtained when the relative distance z between the LFB ultrasonic device and the specimen is changed. FIG. 1 is a cross-sectional view, showing the principle of measurement, of a system including an ultrasonic device, consisting of an ultrasonic transducer 1, an LFB acoustic lens 2, and a glass specimen 3. The focal point, which would be situated in the water, is taken as the origin Oxy for the coordinate axes, as shown in the figure. The ultrasonic plane wave excited by ultrasonic transducer 1 is focused into a wedge shape by LFB acoustic lens 2 and irradiated onto the surface of glass specimen 3 through a water coupler 4. In case the specimen is closer to the ultrasonic device side than a focal plane 5 is, the components predominantly contributed to the output of ultrasonic transducer 1 among the reflected waves from glass substrate 3 will, by the effect of the opening surface of acoustic lens 2, only be the components taking paths P0, P1, P2 approximately shown in FIG. 1. The P0 component is the component directly reflected from the specimen, the P1 component is the component incident on glass specimen 3 at a critical LSAW excitation angle θLSAW propagated as a leaky surface acoustic wave (LSAW) along the surface of glass specimen 3. The P2 component is the component incident on glass specimen 3 at a critical LSSCW excitation angle θLSSCW propagated as a leaky surface-skimming compressional wave (LSSCW) along the surface of glass specimen 3. The transducer output V(z) is obtained as the interference waveform of these three components. In the V(z) curve analysis model (Non-Patent Reference 5), it is approximately expressed by the following equation:V(z)=VI(z)(LSAW)+VI(z)(LSSCW)+VL(z)  (1)whereVL(z)=VL′(z)+ΔVL(z)  (2)and VI(z)(LSAW) and VI(z)(LSSCW) are the respective LSAW and LSSCW interference components, and VL(Z) is the component reflecting the characteristics of the ultrasonic device. Also, ΔVL(Z) is the difference of VL(z) with respect to VL′(z) of a specimen with no excitation of leaky acoustic waves (e.g. Teflon®). VI(z)(LSAW) and VI(z)(LSSCW) are extracted on the basis of the V(z) curve analysis method (Non-Patent Reference 5), and their interference intervals ΔzLSAW and ΔzLSSCW are obtained and substituted for Δz in Eq. (3), which follows, to obtain the LSAW velocity VLSAW and the LSSCW velocity VLSSCW.
                    V        =                              V            W                                              1              -                                                (                                      1                    -                                                                  V                        W                                                                                              2                          ⁢                          f                          ⁢                                                                                                          ⁢                          Δ                          ⁢                                                                                                          ⁢                          z                                                ⁢                                                                                                                                                        )                                2                                                                        (        3        )            where f is the ultrasonic frequency and VW is the longitudinal velocity in water. VW can be obtained, according to Non-Patent Reference 6, from the water coupler temperature measured by means of a thermocouple at the time of the V(z) curve measurement.
Next, the procedure of extracting the LSAW velocity VLSAW and the LSSCW velocity VLSSCW by the V(z) curve analysis method will be explained using the flowchart shown in FIG. 2. It will be explained by considering the V(z) curve measured at f=225 MHz for ultra-low-expansion glass #1 (made by Company A).
Step S1: Normally, the V(z) curve measured on a decibel scale (FIG. 3A) is converted into a digital waveform, loaded to a computer, and converted to a linear scale (FIG. 3B).
Step S2: VW is obtained with Non-Patent Reference 6 from the water coupler temperature TW measured at the same time as the V(z) curve.
Step S3: The VL′(z) curve (e.g. V(z) curve measured for Teflon® (FIG. 3C)), which is a curve approximating the VL(Z) curve reflecting the characteristics of the ultrasonic device, is obtained, and by subtracting from the V(z) curve of Step S1, the VI′(z) curve is obtained (FIG. 4A). Consequently, the result from Eqs. (1) and (2) is that
                                                                                          V                  I                  ′                                ⁡                                  (                  z                  )                                            =                                                V                  ⁡                                      (                    z                    )                                                  -                                                      V                    L                    ′                                    ⁡                                      (                    z                    )                                                                                                                          =                                                                                          V                      I                                        ⁡                                          (                      z                      )                                                        ⁢                                      (                    LSAW                    )                                                  +                                                                            V                      I                                        ⁡                                          (                      z                      )                                                        ⁢                                      (                    LSSCW                    )                                                  +                                  Δ                  ⁢                                                                          ⁢                                                            V                      L                                        ⁡                                          (                      z                      )                                                                                                                              (                  3          ⁢          a                )            is obtained.
Step S4: For the VI′(z) curve of Step S3, the interference component due to LSAW (the interference interval ΔzLSAW) is removed by using a digital filter, and the VI″(z) curve expressing the low-frequency component including the direct current component is extracted (FIG. 5A). Consequently, from Eq. (3a) above, the result is thatVI″(z)=VI′(z)−VI(z)(LSAW)=VI(z)(LSSCW)+ΔVL(Z)  (3b)is obtained.
Step S5: By subtracting the VI″(z) curve obtained in Step S4 from the VI′(z) curve obtained in Step S3, the interference output curve VI(z)(LSAW) needed for the LSAW analysis is obtained (FIG. 4B). Specifically,VI(z)(LSAW)=VI′(z)−VI″(z).  (3c)
Step S6: By performing an FFT (Fast Fourier Transform) analysis of the VI(z)(LSAW) curve obtained in Step S5, in the FFT analysis range shown in FIG. 4B, a wavenumber spectrum distribution is obtained (FIG. 4C), and from its peak value, the interference interval ΔzLSAW is determined.
Step S7: From ΔzLSAW obtained in Step S6 and VW obtained in Step S2, VLSAW is determined from Eq. (3).
Step S8: From VI″(z) obtained in Step S4, the interference component due to LSSCW (the interference interval ΔzLSSCW) is removed by using a digital filter, and the ΔVL(z) curve including the direct current component is extracted (FIG. 5B).
Step S9: By subtracting ΔVL(Z) obtained in Step S8 from VI″(z) obtained in Step S4, the interference output curve VI(z)(LSSCW) required for the LSSCW analysis is obtained (FIG. 5C).
Step S10: By performing an FFT analysis in the FFT analysis range shown in FIG. 5C of the VI(z)(LSSCW) curve obtained in Step S9, the wavenumber spectrum distribution (FIG. 5D) is obtained, and the interference interval ΔzLSSCW is determined from its peak value.
Step S11: From ΔzLSSCW obtained in Step S10 and VW obtained in Step S2, VLSSCW is determined from Eq. (3).
Since, so far, in the materials evaluation using VLSAW, materials having small acoustic losses and exhibiting no velocity dispersion (e.g. single crystal materials) were mainly targeted, an analytical method with respect to ultra-low-expansion glasses, which have the possibility of having large such losses and exhibiting velocity dispersion, was not developed. Since the leaky acoustic wave velocities (VLSAW and VLSSCW) obtained by the V(z) curve analysis method depend on the system and the ultrasonic device and are shifted from the true value, it is necessary to perform an absolute calibration using a standard specimen, as shown in Non-Patent Reference 7. In that calibration method, a numerical calculation of the propagation characteristics of the leaky acoustic waves is necessary, but the calculation was performed, based on Non-Patent Reference 8 or Non-Patent Reference 9, by assuming the specimen and the water to be lossless and by disregarding velocity dispersion and the attenuation coefficients. That is to say that a preparation method for an appropriate standard specimen with respect to materials with the possibility of having large acoustic losses and presenting velocity dispersion has not been investigated.
Evaluation methods of the coefficient of thermal expansion based on conventional methods had the problems of having a low measurement accuracy, not being able to non-destructively evaluate specimen with shapes actually utilized, and not being able to measure distribution characteristics. Moreover, as to materials evaluation based on an LFB ultrasonic material characterization system, for which there can be expected a higher measurement accuracy than for conventional methods and the implementation, non-destructively and without contact, of measurements of the distribution characteristics in the surface of material substrates, an analytical method with respect to ultra-low-expansion glass materials having the possibility of exhibiting velocity dispersion characteristics has not been developed.
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